Question

(A) If \(\frac{1}{x}:\frac{1}{y}:\frac{1}{z}\) =2: 3: 5, then x:y:z = 15:10: 6
(B) If 4p = 6q = 9r then p:q:r = :9:6:4
(C) If 2A = 3B = 4C then A:B:C = 3:4:6
(D) P:Q:R = 2:3:4 then \(\frac{P}{Q}:\frac{Q}{R}:\frac{R}{P}\)=9:8:24
Choose the correct answer from the options given below:

• (C) only
• (D) only
• (A) and (B) only
• (C) and (D) only

Answer 1

The Correct Option is C

Statement (A) is correct. If \( \frac{1}{x} : \frac{1}{y} : \frac{1}{z} = 2 : 3 : 5 \), then the ratio \( x : y : z \) will be the inverse of these values, resulting in \( x : y : z = 15 : 10 : 6 \).
Statement (B) is also correct. If \( 4p = 6q = 9r \), we can write the ratios as \( p : q : r = 9 : 6 : 4 \).
Statement (C) is incorrect. The correct ratio \( A : B : C = 3 : 4 : 6 \) should be derived by solving the equation \( 2A = 3B = 4C \), which doesn’t lead to the given ratio.
Statement (D) is incorrect because simplifying \( P / Q : Q / R \) does not result in the ratio \( 9 : 8 : 24 \).